| Liabilities | Amount (₹) | Assets | Amount (₹) |
|---|---|---|---|
| Sundry Creditors | 1,80,000 | Cash in hand | 30,000 |
| General Reserve | 20,000 | Debtors | 1,20,000 |
| Capitals: | Kishore – 6,00,000 | Stock | 1,50,000 |
| Ranjan – 4,00,000 | Furniture | 1,00,000 | |
| Land and Building | 8,00,000 | ||
| Total | 12,00,000 | Total | 12,00,000 |
Journal Entries in the books of the firm:
| Particulars | L.F. | Amount (₹) |
|---|---|---|
| Cash A/c Dr. To Singh's Capital A/c To Premium for Goodwill A/c (Being capital and goodwill premium brought in by Singh) | 2,00,000 1,50,000 50,000 | |
| Premium for Goodwill A/c Dr. To Kishore's Capital A/c To Ranjan's Capital A/c (Being goodwill premium distributed in sacrificing ratio 3:2) | 50,000 30,000 20,000 | |
| Revaluation A/c Dr. To Stock A/c To Furniture A/c To Provision for Doubtful Debts A/c To Creditors A/c (Being decrease in assets and provision created) | 38,000 15,000 10,000 6,000 1,000 | |
| Land and Building A/c Dr. Investments A/c Dr. To Revaluation A/c (Being increase in assets recorded) | 80,000 10,000 90,000 | |
| Revaluation A/c Dr. To Kishore’s Capital A/c To Ranjan’s Capital A/c (Being profit on revaluation distributed in 3:2) | 52,000 31,200 20,800 | |
| General Reserve A/c Dr. To Kishore’s Capital A/c To Ranjan’s Capital A/c (Being general reserve distributed in old ratio) | 20,000 12,000 8,000 |
Balance Sheet of Atharv and Anmol as at 31st March, 2024
| Liabilities | Amount (₹) | Assets | Amount (₹) |
|---|---|---|---|
| Capitals: | Fixed Assets | 14,00,000 | |
| Atharv | 8,00,000 | Stock | 4,90,000 |
| Anmol | 4,00,000 | Debtors | 5,60,000 |
| General Reserve | 3,50,000 | Cash | 10,000 |
| Creditors | 9,10,000 | ||
| Total | 24,60,000 | Total | 24,60,000 |
Aryan and Adya were partners in a firm sharing profits and losses in the ratio of 3 : 1. Their Balance Sheet on 31st March, 2024 was as follows :
Balance Sheet (Before Dev's Admission)
| Liabilities | Amount (₹) | Assets | Amount (₹) |
|---|---|---|---|
| Capital: Aryan | 3,20,000 | Machinery | 3,90,000 |
| Capital: Adya | 2,40,000 | Furniture | 80,000 |
| Workmen’s Compensation Reserve | 20,000 | Debtors | 90,000 |
| Bank Loan | 60,000 | Less: Provision for Doubtful Debts | (1,000) |
| Creditors | 48,000 | Net Debtors | 89,000 |
| Stock | 77,000 | ||
| Cash | 32,000 | ||
| Profit and Loss A/c | 20,000 | ||
| Total | ₹6,88,000 | Total | ₹6,88,000 |
A racing track is built around an elliptical ground whose equation is given by \[ 9x^2 + 16y^2 = 144 \] The width of the track is \(3\) m as shown. Based on the given information answer the following: 
(i) Express \(y\) as a function of \(x\) from the given equation of ellipse.
(ii) Integrate the function obtained in (i) with respect to \(x\).
(iii)(a) Find the area of the region enclosed within the elliptical ground excluding the track using integration.
OR
(iii)(b) Write the coordinates of the points \(P\) and \(Q\) where the outer edge of the track cuts \(x\)-axis and \(y\)-axis in first quadrant and find the area of triangle formed by points \(P,O,Q\).